A quantitative complexity theory of human-computer interaction is presented and validated by means of laboratory experiments. Based on the seminal work of Grassberger in theoretical physics, a complexity measure is introduced. The measure is termed the Effective Measure Complexity and has three main advantages. First, it relies solely on information-theoretic quantities, which are intimately connected with the concept of complexity and not randomness. Second, it is model independent and can be estimated efficiently from data. Third, the estimates can be derived from behavioural patterns in terms of observable interaction events alone. Subjective ratings or psychophysiological measurements can be included but are not mandatory. In order to explain the theory, a simple and easy to generalise example in mobile human-computer interaction is presented. Furthermore, the external validity of the complexity measure is studied in laboratory experiments. The experimental task was to search for multiple targets on an electronic chart display and information system (ECDIS). ECDIS is an integral component of modern ship bridge concepts and therefore the experiments were carried out in a marine simulator. Thirty users participated. The platform motion (with or without motion) and the workplace illumination (800 lux or 30 lux) were varied systematically and the complexity effects were studied. The results show that the complexity of the visual search processes is significantly lower when the simulator is put in sea state characteristics and the users are facing straining motion forces. In addition, interaction complexity is significantly lowered when illuminance is reduced from the daylight level of 800 lux to the twilight level of 30 lux. Therefore, the complexity measure seems to be a valid for the quantitative assessment of human-computer interaction.